MODELLING THE COLLATZ PROBLEM FROM A JACOBSTHAL VIEWPOINT

This work does not aim to solve the Collatz conjecture, but to reformulate it within a new analytical framework based on Jacobsthal sequences. This reformulation reveals structural regularities and symmetries that remain hidden in the traditional approach, offering a new mathematical perspective from which the Collatz-type problems may be further explored. This approach can be reproduced in System Engineering analyses, where alternative representation are often valuable for exposing hidden structure and improving understanding. Beyond its mathematical significance, the proposed framework may also offer conceptual and methodological benefits for the field of Information Technology (IT). Many problems in computer science involve the analysis of iterative processes, recursive algorithms, and discrete state transitions. The Collatz transformation itself can be viewed as a simple computational process governed by conditional rules and repeated iteration, which makes it an interesting model for studying algorithmic behavior. Sequence-based representations are widely used in areas such as data compression, cryptography, and pseudo-random number generation. The identification of structured recurrence relations and parity patterns within integer sequences can provide insights into the design of efficient algorithms for generating deterministic yet complex numerical sequences. Such sequences are frequently employed in cryptographic systems, simulation models, and distributed computing applications.